Seriously, until you have some practice soldering, and soldering smaller circuits in particular, DO NOT try to solder a PS2 modchip. Your best bet is to take it to a place that does mods, like an import shop, or just send it to a reputable site that does it. If you do decide to DIY, you should have a magnifying glass (one that stands on its own), good lighting, thin solder, and a tiny tip.
i can't think of a good beginner's soldering project outside of an actual circuit. Most of the pins (the "legs") on the chips you can buy locally are larger than those custom ones they use in consoles, so it'll take a bit more proficiency to do it without screwing something up.
It's simple in theory, but in execution it takes practice to do it well, especially with small circuits. If you only plan to mod your consoles, i'd recommend having someone else do it unless you become really confident in your abilities. This is especially true if you don't have a soldering iron and solder. The money spent in equipment could just as well go into a modding service.